Do you think so? It seems that the strength of the Rebellion has always been in the Rim and various alien traitors. The Rim has always been very marginal, economically speaking; you have a few rich worlds like Onderon in the Inner Rim or Dac which was a rich shipbuilding center in spite of its peripheral position, but for every Onderon or Dac you have a hundred like Tatooine, Dantooine, Kashyyyk, or Saleucami: agrarian or resource-extraction worlds with very little planetary industry, much less the sort of facilities they'd need to exert any meaningful influence beyond their own orbital spheres. Now, by contrast, the Rebels only have limited support from a few core worlds like Alderaan and Chandrila, the former of which was already destroyed even before this hypothetical divergence point. I don't see that changing tremendously in the wake of the destruction of the Death Star, not with the the Imperial Navy still completely intact. In the absolute worst circumstance where the entire Rim rises up simultaneously in the wake of the loss of the Death Star and somehow cuts off all Imperial Navy elements in the Rim, leaving us only with our forces in the Core Worlds, the Empire can still commit itself to a retrenchment before using its superior manufacturing to reduce the periphery one world at a time. They would run rampant for a few years, but I'm not sure they could parley that into any long-term advantage without taking extremely brutal measures that I do not believe their leadership had the political strength to utilize, and even if they did, would cost them any claim to that moral high ground that they were so fond of in their propaganda.
Even if the Death Star were destroyed and, oh, let's go one step further and say that the loss of the Death Star also takes out Admiral Tarkin, Darth Vader, and all of the Joint Chiefs, who I should remind you were also aboard the Death Star, these people do not exist in a vacuum. Even Darth Vader could be replaced, and though I suspect he would be the hardest to replace due to the trust invested in him back then, it may well turn out even better in the long run given his eventual treasonous actions and failure to replace Emperor Palpatine under those old-fashioned Sith rules. For the remainder, replacements could be found and promoted from within the military and COMPNOR without too much difficulty. There wouldn't be any significant dislocation of central authority without Palpatine himself dying, and I suspect he would never be foolish enough to leave his security envelope in Coruscant for any trivial reason.
That said, the destruction of the Death Star would have one outright positive effect in my opinion. In my opinion, Tarkin was a bit too trigger-happy with the thing during his tenure. Alderaan had a popular government unstintingly opposed to the Empire, as was Chandrila. Dac was the heart of the independent Rebel shipbuilding capabilities and, alien-dominated as it was by the Mon Calamari and Quarren, was almost certainly not going to be reconciled to the Empire. Onderon was, however, in a state of open civil war, and would have been better served by direct materiel support to pro-Imperial parties. Fear is all and good, but overuse of fear, especially if it's erratic or not applied in response to consistent stimuli, results in neurosis and even psychosis in extreme cases. Moreover, destroying these worlds only denied their resources to the Empire. That's all and fine in the case of Alderaan, but what if, as a hypothetical, a Rebel cell had somehow risen up and usurped the reins of power on Kuat or, one step further, Coruscant itself? Destroying those worlds would have gutted the Empire, and failing to destroy those worlds would have shown the Tarkin Doctrine to be just words on the wind. The Tarkin Doctrine was ultimately flawed, and its revision or, let's go one step further and suggest maybe even its outright abandonment may have come even sooner had the primary instrument of its implementation been destroyed.